In late October, 1988, a survey was conducted by CBS News of 1500 adults in the United States to find out their preferences in the upcoming presidential election. Out of 1500 persons, y1 = 750 supported George Bush, y2 = 650 supported Michael Dukakis, and y3 = 100 supported other candidates or expressed no opinion. Assume that the data y = (y1,y2,y3) follow the multinomial distribution with parameters (01, 02, 03). a. Find a conjugate prior for (01, 02, 03). b. Define a noninformative prior for (01, 02, 03). c. Assume that p(01, 02, 03) ∞ 010203. Find the posterior distribution of (01, 02, 03) given data y.
In late October, 1988, a survey was conducted by CBS News of 1500 adults in the United States to find out their preferences in the upcoming presidential election. Out of 1500 persons, y1 = 750 supported George Bush, y2 = 650 supported Michael Dukakis, and y3 = 100 supported other candidates or expressed no opinion. Assume that the data y = (y1,y2,y3) follow the multinomial distribution with parameters (01, 02, 03). a. Find a conjugate prior for (01, 02, 03). b. Define a noninformative prior for (01, 02, 03). c. Assume that p(01, 02, 03) ∞ 010203. Find the posterior distribution of (01, 02, 03) given data y.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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